An autographed baseball rolls off of a 1.5m high desk and strikes the floor 0.60m away from the desk.
How fast was it rolling on the desk before it fell? The acceleration of gravity is 9.81m/s^2.
Answer in units of m/s
time to fall 1.5m
h=1/2 a t^2
t=sqrt(2h/a)=sqrt(3.0/9.8) figure that out.
speedhorizontal=distance/time
= .6/time to fall.
To find the speed at which the baseball was rolling on the desk before it fell, we can use the principle of conservation of energy.
When the baseball falls, it converts its potential energy into kinetic energy, neglecting air resistance. The potential energy of an object at a certain height is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
In this case, the potential energy of the baseball at a height of 1.5m is given by PE = mg(1.5m).
When the baseball strikes the floor, all of its potential energy is converted into kinetic energy. The kinetic energy of an object is given by the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
Equating the potential energy to the kinetic energy, we have:
mg(1.5m) = (1/2)mv^2
Canceling out the mass, we have:
9.81m/s^2 * 1.5m = (1/2)v^2
Simplifying, we get:
14.715 m^2/s^2 = (1/2)v^2
Multiplying both sides by 2, we get:
29.43 m^2/s^2 = v^2
Taking the square root of both sides, we get:
v ≈ √29.43 m^2/s^2
v ≈ 5.43 m/s
Therefore, the speed at which the baseball was rolling on the desk before it fell was approximately 5.43 m/s.